A Subdivision Framework for Partition of Unity Parametrics
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Full frame distilled prediction
Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Theoretical or conceptualConsensus signal: none
- Genre
- Candidate signal: MethodsConsensus signal: none
- Teacher disagreement score
- 0.654
- Threshold uncertainty score
- 0.531
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
- Teacher spread
- 0.256 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
Partition of Unity Parametrics (PUPs) are a generalization of NURBS that allow us to use arbitrary basis functions for modeling parametric curves and surfaces. One interesting problem is finding subdivision schemes for this recently developed and flexible class of parametrics. In this paper, we introduce a systematic approach for determining uniform subdivision of PUPs curves and tensorproduct surfaces. Our approach formulates PUPs subdivision as a least squares problem, which enables us to find exact subdivision filters for refinable basis functions and optimal approximate schemes for irrefinable ones. To illustrate this approach, we provide sample subdivision schemes with different properties, which are further demonstrated by presenting various examples.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
The record
- Venue
- Canada Human-Computer Communications Society
- Topic
- Advanced Numerical Analysis Techniques
- Field
- Engineering
- Canadian institutions
- University of Calgary
- Funders
- not available
- Keywords
- SubdivisionGeneralizationPartition (number theory)Parametric statisticsBasis (linear algebra)Subdivision surfaceClass (philosophy)Partition of unity
- Has abstract in OpenAlex
- yes